Problem: What do the following two equations represent? $-x-4y = -5$ $12x-3y = -4$
Answer: Putting the first equation in $y = mx + b$ form gives: $-x-4y = -5$ $-4y = x-5$ $y = -\dfrac{1}{4}x + \dfrac{5}{4}$ Putting the second equation in $y = mx + b$ form gives: $12x-3y = -4$ $-3y = -12x-4$ $y = 4x + \dfrac{4}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.